Damage in composite laminates affects its overall viscoelastic response. Constitutive equations have been developed for composite laminates considering a fixed damage state. A complete description, however, requires suitable damage evolution laws. This paper is focused on studying damage evolution in viscoelastic laminates using a cohesive finite element approach. A two dimensional, four nodded finite element is developed incorporating a rate-independent traction-displacement cohesive law. This element is used in conjunction with plane strain bulk elements behaving in a linear viscoelastic manner to simulate crack evolution between two existing transverse cracks in symmetric cross-ply laminates. The effects of loading strain-rate, ply constraint and initial crack density are studied. This study shows expected trends in the behavior and indicates the suitability of cohesive zone modeling to study damage evolution in viscoelastic composite materials.